A139706 Take n in binary. Rotate the binary digits to the right until a 1 once again appears as the leftmost digit. Convert back into decimal for a(n).

1, 2, 3, 4, 6, 5, 7, 8, 12, 10, 13, 9, 14, 11, 15, 16, 24, 20, 25, 18, 26, 21, 27, 17, 28, 22, 29, 19, 30, 23, 31, 32, 48, 40, 49, 36, 50, 41, 51, 34, 52, 42, 53, 37, 54, 43, 55, 33, 56, 44, 57, 38, 58, 45, 59, 35, 60, 46, 61, 39, 62, 47, 63, 64, 96, 80, 97, 72, 98, 81, 99, 68

Offset: 1

Author

Leroy Quet, Apr 30 2008

Keywords

• nonn
• base
• easy

Comments

This sequence written in binary is A139707.

This is a permutation of the positive integers. A139708 is the inverse permutation.

Moreover, the first 2^n terms are a permutation of the first 2^n positive integers. Fixed points of the permutation are A272919. - Ivan Neretin, May 10 2016

Links

• Ivan Neretin, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A139707 (in binary), A139708 (inverse), A272919 (fixed points).

Programs

Maple

A139706 := proc(n) local a; a := ListTools[Rotate](convert(n,base,2),1) ; while op(-1,a) = 0 do a := ListTools[Rotate](a,1) ; od: add(op(i,a)*2^(i-1),i=1..nops(a)) : end: seq(A139706(n),n=1..100) ; # R. J. Mathar, May 04 2008

Mathematica

Table[FromDigits[RotateRight[IntegerDigits[n, 2], IntegerExponent[n, 2] + 1], 2], {n, 72}] (* Ivan Neretin, May 10 2016 *)

Extensions

More terms from R. J. Mathar, May 04 2008